1. Field of the Invention
The present invention relates to a system identification apparatus for identifying a system such as an attitude control system of an artificial satellite.
2. Description of the Prior Art
The typical system identification apparatus employs, for example, a frequency response method in identifying dynamic characteristics of a system. The frequency response method is based on a fact that sine wave input and output signals received and outputted by a control system to be identified have the same frequency. Gain and phase characteristics of the control system with respect to the frequency are found from this fact.
Some system identification apparatuses directly find such frequency characteristics according to a fast Fourier transform (FFT) method. The FFT method is effective only when there is less observation noise and ineffective when there is so much observation noise that it may deteriorate the identification accuracy of the FFT method.
To improve the identification accuracy of the FFT method, one method has been proposed. This method averages the influence of the observation noise, identifies parameters of an objective control system in a time domain according to the method of least squares and, according to the identified parameters, calculates the frequency characteristics of the control system.
Even with the FFT method, it is difficult to identify the characteristics of a control system of, for example, an artificial satellite that is bulky and light in weight and has oscillation characteristics involving many oscillation modes of poor attenuation. In particular, the oscillation mode of port attenuation has a resonance point and an antiresonance point having entirely different energy levels and, therefore, is difficult to identify.
In an oscillation system, a signal energy level drastically differs in a rigid mode and an oscillating mode of the system. This is the reason why it is difficult to numerically identify characteristics of the oscillation system.
To identify characteristics of such an oscillation system, one identification apparatus has been proposed. This apparatus does not identify characteristics of the system for an entire frequency band at a time but divides the frequency band into several sections through a plurality of band-pass filters having different passbands, and applies the method of least squares for each of the frequency band sections, thereby identifying characteristics of each of the frequency band sections of the control system. This apparatus can accurately identify characteristics of an oscillating mode of the control system, but there is a problem in empirically selecting the plurality of band-pass filters having different passbands. This empirical selection prevents an improvement in the accuracy of identification of the apparatus. In addition, this apparatus takes a long time for identification.
As described above, the apparatus employing the FFT method hardly identifies characteristics of a control system accurately when there is a great deal of observation noise. The averaging method may reduce the influence of the observation noise in identifying the characteristics of a control system in a time domain. The averaging method, however, is not applicable, as it is, for accurately identifying characteristics of a control system such as an artificial satellite that is bulky and light weight and has oscillation characteristics involving many oscillation modes of poor attenuation.
To accurately identify characteristics of such oscillation modes of the system, it may be effective to properly select band-pass filters to identify characteristics of each frequency band of the system. The band-pass filters, however, must be selected empirically, thereby hindering an improvement of accuracy. In addition, this method takes a long time for identification.